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codes/quantum/qudits_galois/stabilizer/topological/galois_topological.yml
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####################################################### | ||
## This is a code entry in the error correction zoo. ## | ||
## https://github.com/errorcorrectionzoo ## | ||
####################################################### | ||
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code_id: galois_topological | ||
physical: galois | ||
logical: galois | ||
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name: 'Galois-qudit surface code' | ||
introduced: '\cite{arxiv:quant-ph/0609070,arxiv:1202.3338}' | ||
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alternative_names: | ||
- '\(\mathbb{F}_q\)-qudit surface code' | ||
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description: | | ||
Extension of the surface code to 2D lattices of Galois qudits. | ||
relations: | ||
parents: | ||
- code_id: galois_css | ||
- code_id: 2d_stabilizer | ||
- code_id: generalized_homological_product_css | ||
- code_id: quantum_double | ||
detail: 'A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Galois-qudit surface codes yield Abelian quantum-double codes with \(GF(p^m)\cong \mathbb{Z}_p^m\) topological order via this decomposition.' | ||
cousins: | ||
- code_id: quantum_double_abelian | ||
detail: 'A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits \cite{doi:10.1109/18.959288}\cite[Sec. 5.3]{arxiv:quant-ph/0501074}\cite{preset:GottesmanBook}. Galois-qudit surface codes yield Abelian quantum-double codes with \(GF(p^m)\cong \mathbb{Z}_p^m\) topological order via this decomposition.' | ||
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# Begin Entry Meta Information | ||
_meta: | ||
# Change log - most recent first | ||
changelog: | ||
- user_id: VictorVAlbert | ||
date: '2022-07-27' |